chars_digits([], []).
chars_digits([C|Cs], [D|Ds]) :-
    char_type(C, digit(D)),
    chars_digits(Cs, Ds).

read_file(Stream, []) :-
    at_end_of_stream(Stream).
read_file(Stream, [X|L]) :-
    \+ at_end_of_stream(Stream),
    read_line_to_codes(Stream, C),
    chars_digits(C, X),
    read_file(Stream, L).

main :-
    open('../input/03', read, Stream),
    read_file(Stream, Lines), !,
    close(Stream),
    most_solve(Lines, A),
    least_solve(Lines, B),
    bin_dec(A, A1),
    bin_dec(B, B1),
    X is A1 * B1,
    print([A1, B1, X]).

first_elements([], []).
first_elements([[X|_]|As], [B|Bs]) :-
    first_elements(As, Bs),
    B is X.
last_elements([], _, []).
last_elements([[X|Xs]|As], X, [Xs|Bs]) :-
    last_elements(As, X, Bs).
last_elements([[X|_]|As], F, Bs) :-
    F =\= X,
    last_elements(As, F, Bs).

freq([], 0, 0).
freq([1|As], Z, O) :-
    freq(As, Z, O1),
    O is O1 + 1.
freq([0|As], Z, O) :-
    freq(As, Z1, O),
    Z is Z1 + 1.
 
most_common(A, 1) :-
    freq(A, Z, O),
    O >= Z.
most_common(A, 0) :-
    freq(A, Z, O),
    O < Z.
least_common(A, 0) :-
    freq(A, Z, O),
    Z > 0,
    (O >= Z; O = 0).
least_common(A, 1) :-
    freq(A, Z, O),
    O > 0,
    (O < Z; Z = 0).

first_elem([A|_], A).

most_solve(A, [B]) :-
    first_elements(A, F),
    most_common(F, B),
    first_elem(A, N),
    length(N, 1).
most_solve(A, [B|Bs]) :-
    first_elements(A, F),
    most_common(F, B),
    last_elements(A, B, L),
    most_solve(L, Bs).

least_solve(A, [B]) :-
    first_elements(A, F),
    least_common(F, B),
    first_elem(A, N),
    length(N, 1).
least_solve(A, [B|Bs]) :-
    first_elements(A, F),
    least_common(F, B),
    last_elements(A, B, L),
    least_solve(L, Bs).

bin_dec(B, X) :-
    bin_dec(B, 0, X).
bin_dec([], X, X).
bin_dec([B|Bs], N, X) :-
    M is N * 2 + B,
    bin_dec(Bs, M, X).